A universal quantum wave equation that yields Dirac, Klein-Gordon, Schrodinger and quantum heat equations is derived. These equations are related by complex transformation of space, time and mass. The new symmetry exhibited by these equations is investigated. The universal quantum equation yields Dirac equation in two ways: firstly by replacing the particle my m0 by im0, and secondly by changing space and time coordinates by it and i r, respectively.

No abstract

We have considered a cosmological model with a phenomenological model for the cosmological constant of the form Λ = βR R , β is a constant. For age parameter consistent with observational data the Universe must be accelerating in the presence of a positive cosmological constant. The minimum age of the Universe is H −1 0 , where H 0 is the present Hubble constant. The cosmological constant is found to decrease as t −2 . Allowing the gravitational constant to change with time leads to an ever increasing gravitational constant at the present epoch. In the presence of a viscous fluid this decay law for Λ is equivalent to the one with Λ = 3αH 2 (α = const.) provided α = β 3(β−2) . The inflationary solution obtained from this model is that of the de-Sitter type.

A quaternionic wavefunction consisting of real and scalar functions is found to satisfy the quaternionic momentum eigen value equation. Each of these components is found to satisfy a generalized damped wave equation. This reduces to the massless Klein-Gordon equation for certain cases. For a plane wave solution the angular frequency is complex. This equation is in agreement with the Einstein energy-momentum formula. The spin of the particle is obtained from the interaction of the particle with the photon field

The consequences of the cosmological constant snssts of Csrvslho, Lima, sad Wsgs (A 3PH + 37R ) sre investigated in an extension of the nonsingulsr Ozer-Tshs cosmology. The considered model describes a closed singularity-kee universe evolving through successive epochs of pure radiation, matter generation, and radiation and matter. The early phase of the last period is shown to be s concrete realization of the postslngulsrity radiation ers scenario of Freeze, Adams, Prieman, and Mottola. PACS number(s): 98.80. Cq, 98.80.Hw X. INTRODUCTION Carvalho, Lima, and Waga [1] have proposed the cosmological constant phenomenological ansatz where p and p are the cosmic energy density and pressure, respectively, and It the curvature index. Combining Eq. (3) and the differentiated form of Eq.(2) one has the energy (= E = pRs) equation II. NONSINGULAR MODELIn a Robertson-Walker»~averse with a perfect-Suid energy-moment»~tensor, Einstein's equations with a variable A give (n = 3/Sz G) a p=~-+ --A(t), (R) Rz 3(2) -" ('+")-R +R R where P and p are dimensionless numbers of the order of unity (natural units being used) R is the RobertsonWs&er scale factor, and H = R/R is Hubble's constant (an overdot denotes time &i&erentiation). Equation (1), a consequence of simple dimensional arguments consistent with quantum gravity [1], generalizes an earlier form, A oc R, suggested by Ozer and Taha [2] and also by Chen and Wu [3].Although the Ozer-Taha (OT) and Chen-Wu (CW) models postulate the same type of variation for A, the resulting cosmological scenarios are not similar. In one case (OT) one has a nonsingular universe with a cold beginning and an early phase transition, in the other (CW) a singular big-bang scenario. These differences are due to the model's difFerent initial conditions and the assignment of opposite signs to a certain integration constant.Carvslbo, Lima, and Waga [1] studied the modifications introduced by the P term in Eq. (1) on the cosmology of Chen and Wu. In this work we investigate the effect of this term in an extended Ozer-Taha cosmology. Also from Eqs. (1) and (2), I~' pp+ 1-In the radiation-(p = p/3) dominated (RD) universe Eqs. (1) -(3) yield (p g 2, p"= so. 'A, and Ao a constant) [1] g2 + + g~-2+4P 1 -2P (6)1-2P R +a(l -P)A R 4+~ ( 7) = ' P"R +PAR-1-2P For Ao & 0, p ( 1, the singular cosmological model based on these equations was studied by Car~&o, Lima, and Waga [1]. Here we investigate a scenario obtained by requiring Ao (0 and for which the model is nonsingular. For simplicity and physical relevance [4] we take p & 0 (tshing P = 0, Ao ( 0, P = h = 1 reProduces the nonsingular OT [2] model). A»mverse with a nonvanishing mi~~mum scale factor Ro at t = 0 arises Rom Eq. (6) if Ao ( 0, P ( z~, and k ( 2p. Then from Eq. (7), po -o.